Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24

3x + 5y = 100

Answer 1

The test contains 10 three-point questions and 14 five-point questions.

Answer 2

Let 'x+y=24' be equation 1
and 
'3x+5y=100' be equation 2

multiply equation 1 by 3
so     3x+3y=72       (this is equation 3)
then subtract equation 2 from 3
  3x+3y=72
- 3x-5y=-100
----------------------
      -2y=-28
divide by 2 on both sides
     -2y/2 = -28/2
  -y = - 14
if -y= -14 then   +y=+14
then put y in equation 1(or 2, you have a choice but 1 is easier)
which will be 
x+y= 24
x+14=24
                 minus 14 on both sides
x+14-14= 24-14
                    so
x=10
y=14 and x= 10 your answer
however on the exam paper you would write it like this : 

 'x +y  =24'   ⇒1
'3x+5y=100' ⇒2
    x equation 1 by 3
3x+3y=72
subtract equation 2 from 3
  3x+3y=72
- 3x-5y=-100
----------------------
      -2y=-28
-2y/2 = -28/2
  -y = - 14
if -y= -14 then   +y=+14
put y in equation 1
x+y= 24
x+14=24
x+14-14= 24-14
x=10

y=14 so 5 point answers and x=10 3 point answers

I know its long but you need to understand this. 
Hope it helped :)